Question

In the figures given below, some congruent parts are indicated by identical marks.
(1) Write the test of congruence by which the pairs of triangle in each figure is congruent.
(2) Write proper correspondence between the vertices of triangle while writing the names of triangle.
(3) Also write the remaining congruent parts of the congruent triangle.

(i)

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right) \\ \left(1\right)\mathrm{In}△\mathrm{BAD}\text{and}△\mathrm{BCD}, \\ \angle \mathrm{BDA}=\angle \mathrm{BDC}\left(g\mathrm{iven}\right) \\ \angle \mathrm{BAD}=\angle \mathrm{BCD}\left(g\mathrm{iven}\right) \\ \mathrm{BD}=\mathrm{BD}\left(c\mathrm{ommon}\right) \\ \mathrm{Thus},△\mathrm{BAD}\cong △\mathrm{BCD}(\mathrm{AAS}\mathrm{test}\mathrm{of}\mathrm{congruence}) \\ \left(2\right)\mathrm{B}\leftrightarrow \mathrm{B},\mathrm{A}\leftrightarrow \mathrm{C},\mathrm{D}\leftrightarrow \mathrm{D} \\ \left(3\right)\mathrm{AB}=\mathrm{BC}\left(\mathrm{by}\mathrm{c}.\mathrm{s}.\mathrm{c}.\mathrm{t}\right) \\ \angle \mathrm{ABD}=\angle \mathrm{CBD}\left(\mathrm{by}\mathrm{c}.\mathrm{a}.\mathrm{c}.\mathrm{t}\right) \\ \mathrm{AD}=\mathrm{DC}\left(\mathrm{by}\mathrm{c}.\mathrm{s}.\mathrm{c}.\mathrm{t}\right) \end{gathered}$$